Prepared by, Brijrajsinh Sarvaiya(13ME548) Jaypalsinh Jadeja(13ME517) Pradipsinh Jadeja(13ME518) Virendrasinh Parmar(13ME539) Gas power cycle

Objectives 1. Evaluate the performance of gas power cycles. 2. Develop simplifying assumptions applicable to gas power cycles. 3. Review the operation of reciprocating engines. 4. Analyze both closed and open gas power cycles. 5. Solve problems based on the Otto and Diesel cycles. 6. Solve problems based on the Brayton cycle; Brayton cycle with regeneration; and Brayton cycle with intercooling, reheating, and regeneration. 7. Identify simplifying assumptions and perform second-law analysis on gas power cycles.

Basic Considerations In Power Cycles Analysis Most power-producing devices operate on cycles. Ideal cycle: A cycle that resembles the actual cycle closely but is made up totally of internally reversible processes is called an ideal cycle. Recall: Thermal efficiency of heat engines Reversible cycles such as Carnot cycle have the highest thermal efficiency of all heat engines operating between the same temperature levels. Unlike ideal cycles, they are totally reversible, and unsuitable as a realistic model. The analysis of many complex processes can be reduced to a manageable level by utilizing some idealizations.

Idealizations (simplifications) in the analysis of power cycles. Care should be exercised in the Interpretation of the results from ideal cycles. On a T - s diagram, the ratio of the area enclosed by the cyclic curve to the area under the heat-addition process curve represents the thermal efficiency of the cycle. 1.The cycle does not involve any friction. Therefore, the working fluid does not experience any pressure drop as it flows in pipes or heat exchangers. 2.All expansion and compression processes take place in a quasi-equilibrium manner. 3.The pipes connecting the various components of a system are well insulated, so heat transfer through them is negligible. On both P-v and T - s diagrams, the area enclosed by the process curve represents the net work of the cycle.

Basic Components The piston reciprocates in the cylinder between two fixed positions called the top dead centre (TDC) - the position that forms the smallest volume in the cylinder - and the bottom dead centre (BDC) - position that forms the largest volume in the cylinder. The distance between TDC and BDC is called the stroke of the engine. The diameter of the piston is called the bore. Compression ratio:

Performance Characteristics Net work output per cycle: Mean effective pressure (MEP): A fictitious pressure that, if it is acted on the piston during the entire power stroke, would produce the same amount of net work as that produced during the actual cycle. Classifications of IC Engines : 1. Spark-ignition (SI) or Petrol engines 2. Compression-ignition (CI) or Diesel engines

Otto Cycle: Ideal Spark-Ignition Engines Cycle The piston executes four complete strokes within the cylinder. The crankshaft completes two revolutions for each thermodynamic cycle. These engines are called four-stroke IC engines. Actual and ideal cycles in spark-ignition engines on a P-v diagram.

T - s Diagram of Ideal Otto Cycle Sequence of processes: IC Engines Classifications: Four-stroke cycle 1 cycle = 4 stroke = 2 revolutions of crankshaft Two-stroke cycle 1 cycle = 2 stroke = 1 revolution of crankshaft

Thermal Efficiency of Otto Cycle The heat supplied to the working fluid during constant- volume heating (combustion), The heat rejected from the working fluid during constant-volume cooling (exhaust), Temperature-volume relation, Thermal efficiency, Cold-air standard assumption. Compression ratio,

Engine Knock (Auto ignition) Premature ignition of the fuel produces audible noise called engine knock. It hurts performance and causes engine damage. Auto ignition places upper limit on compression ratios that can be used in SI engines. Specific heat ratio, k affects the thermal efficiency of the Otto cycle.

Diesel Cycle: Ideal Cycle for CI Engines In diesel engines, only air is compressed during the compression stroke, eliminating the possibility of autoignition. These engines can be designed to operate at higher compression ratios, typically between 12 and 24. Fuels that are less refined (thus less expensive) can be used in diesel engines. The combustion process takes place over a longer interval - fuel injection starts when the piston approaches TDC and continues during the first part of power stroke. Hence, combustion process in the ideal Diesel cycle is approximated as a constant-pressure heat- addition process.

Sequence of processes: 1-2 Isentropic compression 2-3 Constant-pressure heat addition 3-4 Isentropic expansion 4-1 Constant-volume heat rejection. Note : Petrol and diesel engines differ only in the manner the heat addition (or combustion) process takes place. It is approximated as a constant volume process in the petrol engine cycle and as a constant pressure process in the Diesel engine cycle.

Thermal Efficiency of Diesel Cycle Heat supplied to the working fluid during the constant-pressure heating (combustion), Heat rejected from the working fluid during the constant-volume cooling (exhaust), Thermal efficiency of Diesel cycle (general), Cutoff ratio,

For the same compression ratio, thermal efficiency of Otto cycle is greater than that of the Diesel cycle. As the cutoff ratio decreases, the thermal efficiency of the Diesel cycle increases. When r c =1, the efficiencies of the Otto and Diesel cycles are identical. Thermal efficiencies of large diesel engines range from about 35 to 40 percent. Higher efficiency and lower fuel costs make diesel engines attractive in applications such as in locomotive engines, emergency power generation units, large ships, and heavy trucks.

Modern CI Engine Cycle and the Thermodynamic Dual Cycle A I R Combustion Products Fuel injected at 15 o before TDC Intake Stroke Air TC BC Compression Stroke Power Stroke Exhaust Stroke Q in Q out Compression Process Const pressure heat addition Process Expansion Process Const volume heat rejection Process Actual Cycle Dual Cycle Q in Const volume heat addition Process

Process 1  2 Isentropic compression Process 2  2.5 Constant volume heat addition Process 2.5  3 Constant pressure heat addition Process 3  4 Isentropic expansion Process 4  1 Constant volume heat rejection Dual Cycle Q in Q out

Thermal Efficiency Note, the Otto cycle (r c =1) and the Diesel cycle (  =1) are special cases:

The use of the Dual cycle requires information about either: i)the fractions of constant volume and constant pressure heat addition (common assumption is to equally split the heat addition), or ii) maximum pressure P 3. Transformation of r c and  into more natural variables yields For the same initial conditions P 1, V 1 and the same compression ratio: For the same initial conditions P 1, V 1 and the same peak pressure P 3 (actual design limitation in engines):

Comparison of Otto, Diesel and Dual Cycles: The important variable factors which are used as the basis for comparison of the cycles are compression ratio, peak pressure, heat addition, heat rejection and the net work. In order to compare the performance of the Otto, Diesel and Dual combustion cycles, some of the variable factors must be fixed. In this section, a comparison of these three cycles is made for the same compression ratio, same heat addition, constant maximum pressure and temperature, same heat rejection and net work output. This analysis will show which cycle is more efficient for a given set of operating conditions.

Case 1: Same Compression Ratio and Heat Addition: The Otto cycle , the Diesel cycle 1-2-3'-4'-1 and the Dual cycle 1-2-2”-3”-4”-1 volume are shown in p-V and T- θ diagram in Fig. (a) and (b) respectively for the same compression ratio and heat input.

Same compression ratio and heat addition

From the T-s diagram, it can be seen that Area = Area 5-2-3'- 6’ = Area 5-2-2"-3"-6" as this area represents the heat input which is the same for all cycles. All the cycles start from the same initial state point 1 and the air is compressed from state 1 to 2 as the compression ratio is same. It is seen from the T-s diagram for the same heat input, the heat rejection in Otto cycle (area ) is minimum and heat rejection in Diesel cycle (5-1-4'-6') is maximum.. Consequently, Otto cycle has the highest work output and efficiency. Diesel cycle has the least efficiency and Dual cycle having the efficiency between the two.

One more observation can be made i.e., Otto cycle allows the working medium to expand more whereas Diesel cycle is least in this respect. The reason is heat is added before expansion in the case of Otto cycle and the last portion of heat supplied to the fluid has a relatively short expansion in case of the Diesel cycle.

Case 2: Same Compression Ratio and Heat Rejection: VolumeEntropy Same compression ratio and heat rejection

Efficiency of Otto cycle is given by [Figs.(a) and (b)], otto η =1- Q R Q S Where, Qs is the heat supplied in the Otto cycle and is equal to the area under the curve 2-3 on the T-s diagram. The efficiency of the Diesel cycle is given by, η Diesel = 1- R Q Q S

Where Q’s is heat supplied in the Diesel cycle and is equal to the area under the curve 2-3' on the T-s diagram [Fig. (b)]. From the T-s diagram in Fig., it is clear that Qs > Q’s i.e., heat supplied in the Otto cycle is more than that of the Diesel cycle. Hence, it is evident that, the efficiency of the Otto cycle is greater than the efficiency of the Diesel cycle for a given compression ratio and heat rejection.

Case 3: Same Peak Pressure, Peak Temperature and Heat Rejection: Figures (a) and (b) show the Otto cycle and Diesel cycle 1-2'-3-4 on p-V and T-s coordinates, where the peak pressure and temperature and the amount of heat rejected are the same. The efficiency of the Otto cycle, η otto = 1- Q R Q S

Where, Qs in the area under the curve 2-3 in Fig. (b). The efficiency of the Diesel cycle, 1-2-3'-3-4 is, Diesel η =1 Q QR ′ S

Same peak pressure and temperature

It is evident from Fig. that Qs > Q’s. Therefore, the Diesel cycle efficiency is greater than the Otto cycle efficiency when both engines are built to withstand the same thermal and mechanical stresses.

Case 4: Same Maximum Pressure and Heat Input: Same maximum pressure and heat input.

For same maximum pressure and heat input, the Otto cycle ( ) and Diesel cycle (1-2'-3'-4'-1) are shown on p-V and T-s diagrams in Fig. (a) and (b) respectively. It is evident from the figure that the heat rejection for Otto cycle (area on T-s diagram) is more than the heat rejected in Diesel cycle (1-5-6'-4').

Hence Diesel cycle is more efficient than Otto cycle for the condition of same maximum pressure and heat input. One can make a note that with these conditions, the Diesel cycle has higher compression ratio than that of Otto cycle. One should also note that the cycle which is having higher efficiency allows maximum expansion. The Dual cycle efficiency will be between these two.

Case 5: Same Maximum Pressure and Work Output: The efficiency, η can be written as Refer to T-s diagram in (b). For same work output the area (work output of Otto cycle) and area 1-2'-3'-4' (work output of Diesel cycle) are same. To achieve this, the entropy at 3 should be greater than entropy at 3'. It is clear that the heat rejection for Otto cycle is more than that of diesel cycle. Hence, for these conditions, the Diesel cycle is more efficient than the Otto cycle. The efficiency of Dual cycle lies between the two cycles. η Work done Heat supplied Work done + Heat rejected = = Work done

References:- Reference Material 1. Refer lecture by IIT Madras Prof. U.S.P. Shet, Prof. T. Sundararajan and Prof. J.M. Mallikarjuna 2. Engineering thermodynamics by P.K.NAG 3. Thermodynamic – An Engineering Approach by Yunus A Cengel and Michael A. Boles